Question

Find the inverse Laplace transform of the following functions by using (7.16). $\frac{\mathbf{p}\mathbf{+}\mathbf{1}}{\mathbf{p}\left(p^2+1\right)}$

Short answer

The residues at poles, $\mathit{f}\left(t\right)\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\mathbf{}\mathbf{+}\mathbf{}\mathit{s}\mathit{i}\mathit{n}\mathbf{}\mathit{t}\mathbf{}\mathbf{-}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathbf{}\mathit{t}$

Step-by-step solution

To find the poles of    by denominator.

Using convolution of we have to find the inverse transform.

The given equation is,

Rewrite it equation as,

To find the poles of by denominator as,

Simple poles have the above equation, and